Abstract: We present a taint analysis that can automatically detect
when string operations result in a string that is free of taints, where
all the tainted patterns have been removed. This is an improvement
on the conservative behavior of previous taint analyzers, where a
string operation on a tainted string always leads to a tainted string
unless the operation is manually marked as a sanitizer. The taint
analysis is built on top of a string analysis that uses finite state
automata to approximate the sets of values that string variables can
take during the execution of a program. The proposed approach has
been implemented as an extension of FlowDroid and experimental
results show that the resulting taint analyzer is much more precise
than the original FlowDroid.
Abstract: Radiative forces of greenhouse gases (GHG) increase the temperature of the Earth's surface, more on land, and less in oceans, due to their thermal capacities. Given this inertia, the temperature increase is delayed over time. Air temperature, however, is not delayed as air thermal capacity is much lower. In this study, through analysis and synthesis of multidisciplinary science and data, an estimate of atmospheric temperature increase is made. Then, this estimate is used to shed light on current observations of ice and snow loss, desertification and forest fires, and increased extreme air disturbances. The reason for this inquiry is due to the author’s skepticism that current changes cannot be explained by a "~1 oC" global average surface temperature rise within the last 50-60 years. The only other plausible cause to explore for understanding is that of atmospheric temperature rise. The study utilizes an analysis of air temperature rise from three different scientific disciplines: thermodynamics, climate science experiments, and climactic historical studies. The results coming from these diverse disciplines are nearly the same, within ± 1.6%. The direct radiative force of GHGs with a high level of scientific understanding is near 4.7 W/m2 on average over the Earth’s entire surface in 2018, as compared to one in pre-Industrial time in the mid-1700s. The additional radiative force of fast feedbacks coming from various forms of water gives approximately an additional ~15 W/m2. In 2018, these radiative forces heated the atmosphere by approximately 5.1 oC, which will create a thermal equilibrium average ground surface temperature increase of 4.6 oC to 4.8 oC by the end of this century. After 2018, the temperature will continue to rise without any additional increases in the concentration of the GHGs, primarily of carbon dioxide and methane. These findings of the radiative force of GHGs in 2018 were applied to estimates of effects on major Earth ecosystems. This additional force of nearly 20 W/m2 causes an increase in ice melting by an additional rate of over 90 cm/year, green leaves temperature increase by nearly 5 oC, and a work energy increase of air by approximately 40 Joules/mole. This explains the observed high rates of ice melting at all altitudes and latitudes, the spread of deserts and increases in forest fires, as well as increased energy of tornadoes, typhoons, hurricanes, and extreme weather, much more plausibly than the 1.5 oC increase in average global surface temperature in the same time interval. Planned mitigation and adaptation measures might prove to be much more effective when directed toward the reduction of existing GHGs in the atmosphere.
Abstract: Although South Africa has made good progress in providing basic water and sanitation services to its citizens, there is still a large section of the population that has no access to these services. This paper reviews the performance of the government’s municipal infrastructure grant programme in providing basic water and sanitation services which are part of the constitutional requirements to the citizens. The method used to gather data and information was a desk top study which sought to review the progress made in rolling out the programme. The successes and challenges were highlighted and possible solutions were identified that can accelerate the elimination of the remaining backlogs and improve the level of service to the citizens. Currently, approximately 6.5 million citizens are without access to basic water services and approximately 10 million are without access to basic sanitation services.
Abstract: With the development of intelligent vehicle systems, a high-precision road map is increasingly needed in many aspects. The automatic lane lines extraction and modeling are the most essential steps for the generation of a precise lane-level road map. In this paper, an automatic lane-level road map generation system is proposed. To extract the road markings on the ground, the multi-region Otsu thresholding method is applied, which calculates the intensity value of laser data that maximizes the variance between background and road markings. The extracted road marking points are then projected to the raster image and clustered using a two-stage clustering algorithm. Lane lines are subsequently recognized from these clusters by the shape features of their minimum bounding rectangle. To ensure the storage efficiency of the map, the lane lines are approximated to cubic polynomial curves using a Bayesian estimation approach. The proposed lane-level road map generation system has been tested on urban and expressway conditions in Hefei, China. The experimental results on the datasets show that our method can achieve excellent extraction and clustering effect, and the fitted lines can reach a high position accuracy with an error of less than 10 cm.
Abstract: We design and implement a precise model of string
operations using finite state machine transformers and state
transformers to approximate the values string variables can take
throughout the execution of the program.We use our model to analyze
Android program string variables. Our experimental results show that
our string analysis is very efficient at detecting the contextual effect
of string operations on the string variables. Our model proved to be
very useful when it came to verifying statements about the string
variables of the program.
Abstract: Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.
Abstract: Calcium is an essential element for good growth and development of the organism, and its requirement is increased at school age. Low socio-economic populations of developing countries such as Colombia may have food deficiency of this mineral in schoolchildren that could be reflected in calcium biochemical indicators, bone alterations and anthropometric indicators. The objective of this investigation was to evaluate some calcium biochemical indicators in a group of schoolchildren of low socioeconomic level from Barranquilla city and to correlate with body mass index. 60 schoolchildren aged 7 to 15 years were selected from Jesus’s Heart Educational Institution in Barranquilla-Atlántico, apparently healthy, without suffering from infectious or gastrointestinal diseases, without habits of drinking alcohol or smoking another hallucinogenic substance and without taking supplementation with calcium in the last six months or another substance that compromises bone metabolism. The research was approved by the ethics committee at Universidad del Atlántico. The selected children were invited to donate a blood and urine sample in a fasting time of 12 hours, the serum was separated by centrifugation and frozen at ˗20 ℃ until analyzed and the same was done with the urine sample. On the day of the biological collections, the weight and height of the students were measured to determine the nutritional status by BMI using the WHO tables. Calcium concentrations in serum and urine (SCa, UCa), alkaline phosphatase activity total and of bone origin (SAPT, SBAP) and urinary creatinine (UCr) were determined by spectrophotometric methods using commercial kits. Osteocalcin and Cross-linked N-telopeptides of type I collagen (NTx-1) in serum were measured with an enzyme-linked inmunosorbent assay. For statistical analysis the Statgraphics software Centurium XVII was used. 63% (n = 38) and 37% (n = 22) of the participants were male and female, respectively. 78% (n = 47), 5% (n = 3) and 17% (n = 10) had a normal, malnutrition and high nutritional status, respectively. The averages of evaluated indicators levels were (mean ± SD): 9.50 ± 1.06 mg/dL for SCa; 181.3 ± 64.3 U/L for SAPT, 143.8 ± 73.9 U/L for SBAP; 9.0 ± 3.48 ng/mL for osteocalcin and 101.3 ± 12.8 ng/mL for NTx-1. UCa level was 12.8 ± 7.7 mg/dL that adjusted with creatinine ranged from 0.005 to 0.395 mg/mg. Considering serum calcium values, approximately 7% of school children were hypocalcemic, 16% hypercalcemic and 77% normocalcemic. The indicators evaluated did not correlate with the BMI. Low values were observed in calcium urinary excretion and high in NTx-1, suggesting that mechanisms such as increase in renal retention of calcium and in bone remodeling may be contributing to calcium homeostasis.
Abstract: The following assumptions of the Big Bang theory are challenged and found to be false: the cosmological principle, the assumption that all matter formed at the same time and the assumption regarding the cause of the cosmic microwave background radiation. The evolution of the universe is described based on the conclusion that the universe is finite with a space boundary. This conclusion is reached by ruling out the possibility of an infinite universe or a universe which is finite with no boundary. In a finite universe, the centre of the universe can be located with reference to our home galaxy (The Milky Way) using the speed relative to the Cosmic Microwave Background (CMB) rest frame and Hubble's law. This places our home galaxy at a distance of approximately 26 million light years from the centre of the universe. Because we are making observations from a point relatively close to the centre of the universe, the universe appears to be isotropic and homogeneous but this is not the case. The CMB is coming from a source located within the event horizon of the universe. There is sufficient mass in the universe to create an event horizon at the Schwarzschild radius. Galaxies form over time due to the energy released by the expansion of space. Conservation of energy must consider total energy which is mass (+ve) plus energy (+ve) plus spacetime curvature (-ve) so that the total energy of the universe is always zero. The predominant position of galaxy formation moves over time from the centre of the universe towards the boundary so that today the majority of new galaxy formation is taking place beyond our horizon of observation at 14 billion light years.
Abstract: The goal of option pricing theory is to help the investors
to manage their money, enhance returns and control their financial
future by theoretically valuing their options. However, most of the
option pricing models have no analytical solution. Furthermore,
not all the numerical methods are efficient to solve these models
because they have nonsmoothing payoffs or discontinuous derivatives
at the exercise price. In this paper, we solve the American option
under jump diffusion models by using efficient time-dependent
numerical methods. several techniques are integrated to reduced
the overcome the computational complexity. Fast Fourier Transform
(FFT) algorithm is used as a matrix-vector multiplication solver,
which reduces the complexity from O(M2) into O(M logM).
Partial fraction decomposition technique is applied to rational
approximation schemes to overcome the complexity of inverting
polynomial of matrices. The proposed method is easy to implement
on serial or parallel versions. Numerical results are presented to prove
the accuracy and efficiency of the proposed method.
Abstract: Cold-start is a notoriously difficult problem which
can occur in recommendation systems, and arises when there is
insufficient information to draw inferences for users or items. To
address this challenge, a contextual bandit algorithm – the Fast
Approximate Bayesian Contextual Cold Start Learning algorithm
(FAB-COST) – is proposed, which is designed to provide improved
accuracy compared to the traditionally used Laplace approximation
in the logistic contextual bandit, while controlling both algorithmic
complexity and computational cost. To this end, FAB-COST uses
a combination of two moment projection variational methods:
Expectation Propagation (EP), which performs well at the cold
start, but becomes slow as the amount of data increases; and
Assumed Density Filtering (ADF), which has slower growth of
computational cost with data size but requires more data to obtain an
acceptable level of accuracy. By switching from EP to ADF when
the dataset becomes large, it is able to exploit their complementary
strengths. The empirical justification for FAB-COST is presented, and
systematically compared to other approaches on simulated data. In a
benchmark against the Laplace approximation on real data consisting
of over 670, 000 impressions from autotrader.co.uk, FAB-COST
demonstrates at one point increase of over 16% in user clicks. On
the basis of these results, it is argued that FAB-COST is likely to
be an attractive approach to cold-start recommendation systems in a
variety of contexts.
Abstract: This study explores the possibility of a space station that will occupy a geostationary equatorial orbit (GEO) and create artificial gravity using centripetal acceleration. The concept of the station is to create a habitable, safe environment that can increase the possibility of space tourism by reducing the wide variation of hazards associated with space exploration. The ability to control the intensity of artificial gravity through Hall-effect thrusters will allow experiments to be carried out at different levels of artificial gravity. A feasible prototype model was built to convey the concept and to enable cost estimation. The SpaceX Falcon Heavy rocket with a 26,700 kg payload to GEO was selected to take the 675 tonne spacecraft into orbit; space station construction will require up to 30 launches, this would be reduced to 5 launches when the SpaceX BFR becomes available. The estimated total cost of implementing the Sussex Biocompatible International Space Station (BISS) is approximately $47.039 billion, which is very attractive when compared to the cost of the International Space Station, which cost $150 billion.
Abstract: Sounding rockets are aerospace vehicles that were developed in the mid-20th century, and since then numerous investigations have been executed with the aim of innovate in this type of technology. However, the costs associated to the production of this type of technology are usually quite high, and therefore the challenge that exists today is to be able to reduce them. In this way, the main objective of this document is to present the design process of a Colombian aerospace mission capable to reach the thermosphere using low-cost “Candy” type solid fuel engines. This mission is the latest development of the Uniandes Aerospace Project (PUA for its Spanish acronym), which is an undergraduate and postgraduate research group at Universidad de los Andes (Bogotá, Colombia), dedicated to incurring in this type of technology. In this way, the investigations that have been carried out on Candy-type solid fuel, which is a compound of potassium nitrate and sorbitol, have allowed the production of engines powerful enough to reach space, and which represents a unique technological advance in Latin America and an important development in experimental rocketry. In this way, following the engineering iterative design methodology was possible to design a 2-stage sounding rocket with 1 solid fuel engine in each one, which was then simulated in RockSim V9.0 software and reached an apogee of approximately 150 km above sea level. Similarly, a speed equal to 5 Mach was obtained, which after performing a finite element analysis, it was shown that the rocket is strong enough to be able to withstand such speeds. Under these premises, it was demonstrated that it is possible to build a high-power aerospace mission at low cost, using Candy-type solid fuel engines. For this reason, the feasibility of carrying out similar missions clearly depends on the ability to replicate the engines in the best way, since as mentioned above, the design of the rocket is adequate to reach supersonic speeds and reach space. Consequently, with a team of at least 3 members, the mission can be obtained in less than 3 months. Therefore, when publishing this project, it is intended to be a reference for future research in this field and benefit the industry.
Abstract: Spaceflight is considered the last frontier in terms of science, technology, and engineering. But it is also the next frontier in terms of human physiology and performance. After more than 200,000 years humans have evolved under earth’s gravity and atmospheric conditions, spaceflight poses environmental stresses for which human physiology is not adapted. Hypoxia, accelerations, and radiation are among such stressors, our research involves suborbital flights aiming to develop effective countermeasures in order to assure sustainable human space presence. The physiologic baseline of spaceflight participants is subject to great variability driven by age, gender, fitness, and metabolic reserve. The objective of the present study is to characterize different physiologic variables in a population of STEM practitioners during an aerobatic flight. Cardiovascular and pulmonary responses were determined in Science Astronaut Candidates (SACs) during unusual attitude aerobatic flight indoctrination. Physiologic data recordings from 20 subjects participating in high-G flight training were analyzed. These recordings were registered by wearable sensor-vest that monitored electrocardiographic tracings (ECGs), signs of dysrhythmias or other electric disturbances during all the flight. The same cardiovascular parameters were also collected approximately 10 min pre-flight, during each high-G/unusual attitude maneuver and 10 min after the flights. The ratio (pre-flight/in-flight/post-flight) of the cardiovascular responses was calculated for comparison of inter-individual differences. The resulting tracings depicting the cardiovascular responses of the subjects were compared against the G-loads (Gs) during the aerobatic flights to analyze cardiovascular variability aspects and fluid/pressure shifts due to the high Gs. In-flight ECG revealed cardiac variability patterns associated with rapid Gs onset in terms of reduced heart rate (HR) and some scattered dysrhythmic patterns (15% premature ventricular contractions-type) that were considered as triggered physiological responses to high-G/unusual attitude training and some were considered as instrument artifact. Variation events were observed in subjects during the +Gz and –Gz maneuvers and these may be due to preload and afterload, sudden shift. Our data reveal that aerobatic flight influenced the breathing rate of the subject, due in part by the various levels of energy expenditure due to the increased use of muscle work during these aerobatic maneuvers. Noteworthy was the high heterogeneity in the different physiological responses among a relatively small group of SACs exposed to similar aerobatic flights with similar Gs exposures. The cardiovascular responses clearly demonstrated that SACs were subjected to significant flight stress. Routine ECG monitoring during high-G/unusual attitude flight training is recommended to capture pathology underlying dangerous dysrhythmias in suborbital flight safety. More research is currently being conducted to further facilitate the development of robust medical screening, medical risk assessment approaches, and suborbital flight training in the context of the evolving commercial human suborbital spaceflight industry. A more mature and integrative medical assessment method is required to understand the physiology state and response variability among highly diverse populations of prospective suborbital flight participants.
Abstract: Maternal health outcome is one of the major population development challenges in Sub-Saharan Africa. The region has the highest maternal mortality ratio, despite the progressive economic growth in the region during the global economic crisis. It has been hypothesized that increase in economic growth will reduce the level of maternal mortality. The purpose of this study is to investigate the existence of the negative relationship between health outcome proxy by maternal mortality ratio and economic growth in Sub-Saharan Africa. The study used the Pooled Mean Group estimator of ARDL Autoregressive Distributed Lag (ARDL) and the Kao test for cointegration to examine the short-run and long-run relationship between maternal mortality and economic growth. The results of the cointegration test showed the existence of a long-run relationship between the variables considered for the study. The long-run result of the Pooled Mean group estimates confirmed the hypothesis of an inverse relationship between maternal health outcome proxy by maternal mortality ratio and economic growth proxy by Gross Domestic Product (GDP) per capita. Thus increasing economic growth by investing in the health care systems to reduce pregnancy and childbirth complications will help reduce maternal mortality in the sub-region.
Abstract: The work sought to understand the pattern of movement of contaminant from a continuous point source through soil. The soil used was sandy-loam in texture. The contaminant used was municipal solid waste landfill leachate, introduced as a point source through an entry point located at the center of top layer of the soil tank. Analyses were conducted after maturity periods of 50 and 80 days. The maximum change in chemical concentration was observed on soil samples at a radial distance of 0.25 m. Finite element approximation based model was used to assess the future prediction, management and remediation in the polluted area. The actual field data collected for the case study were used to calibrate the modeling and thus simulated the flow pattern of the pollutants through soil. MATLAB R2015a was used to visualize the flow of pollutant through the soil. Dispersion coefficient at 0.25 and 0.50 m radial distance from the point of application of leachate shows a measure of the spreading of a flowing leachate due to the nature of the soil medium, with its interconnected channels distributed at random in all directions. Surface plots of metals on soil after maturity period of 80 days shows a functional relationship between a designated dependent variable (Y), and two independent variables (X and Z). Comparison of measured and predicted profile transport along the depth after 50 and 80 days of leachate application and end of the experiment shows that there were no much difference between the predicted and measured concentrations as they were all lying close to each other. For the analysis of contaminant transport, finite difference approximation based model was very effective in assessing the future prediction, management and remediation in the polluted area. The experiment gave insight into the most likely pattern of movement of contaminant as a result of continuous percolations of the leachate on soil. This is important for contaminant movement prediction and subsequent remediation of such soils.
Abstract: The increasing generation of saline wastewater through various industrial activities is becoming a global concern for activated sludge (AS) based biological treatment which is widely applied in wastewater treatment plants (WWTPs). As for the AS process, an increase in wastewater salinity has negative impact on its overall performance. The advent of conventional aerobic granular sludge (AGS) or bacterial AGS biotechnology has gained much attention because of its superior performance. The development of algal-bacterial AGS could enhance better nutrients removal, potentially reduce aeration cost through symbiotic algae-bacterial activity, and thus, can also reduce overall treatment cost. Nonetheless, the potential of salt stress to decrease biomass growth, microbial activity and nutrient removal exist. Up to the present, little information is available on saline wastewater treatment by algal-bacterial AGS. To the authors’ best knowledge, a comparison of the two AGS systems has not been done to evaluate nutrients removal capacity in the context of salinity increase. This study sought to figure out the impact of salinity on the algal-bacterial AGS system in comparison to bacterial AGS one, contributing to the application of AGS technology in the real world of saline wastewater treatment. In this study, the salt concentrations tested were 0 g/L, 1 g/L, 5 g/L, 10 g/L and 15 g/L of NaCl with 24-hr artificial illuminance of approximately 97.2 µmol m¯²s¯¹, and mature bacterial and algal-bacterial AGS were used for the operation of two identical sequencing batch reactors (SBRs) with a working volume of 0.9 L each, respectively. The results showed that salinity increase caused no apparent change in the color of bacterial AGS; while for algal-bacterial AGS, its color was progressively changed from green to dark green. A consequent increase in granule diameter and fluffiness was observed in the bacterial AGS reactor with the increase of salinity in comparison to a decrease in algal-bacterial AGS diameter. However, nitrite accumulation peaked from 1.0 mg/L and 0.4 mg/L at 1 g/L NaCl in the bacterial and algal-bacterial AGS systems, respectively to 9.8 mg/L in both systems when NaCl concentration varied from 5 g/L to 15 g/L. Almost no ammonia nitrogen was detected in the effluent except at 10 g/L NaCl concentration, where it averaged 4.2 mg/L and 2.4 mg/L, respectively, in the bacterial and algal-bacterial AGS systems. Nutrients removal in the algal-bacterial system was relatively higher than the bacterial AGS in terms of nitrogen and phosphorus removals. Nonetheless, the nutrient removal rate was almost 50% or lower. Results show that algal-bacterial AGS is more adaptable to salinity increase and could be more suitable for saline wastewater treatment. Optimization of operation conditions for algal-bacterial AGS system would be important to ensure its stably high efficiency in practice.
Abstract: In the operation of power transformers of 110 kV/MV from substations, these are traveled by fault current resulting from MV line damage. Defect electrical contacts are heated when they are travelled from fault currents. In the case of high temperatures when 135 °C is reached, the electrical insulating oil in the vicinity of the electrical faults comes into contact with these contacts releases gases, and activates the electrical protection. To avoid auto-flammability of electro-insulating oil, we designed a security system thermal of electrical contact defects by pouring fire-resistant polyurethane foam, mastic or mortar fire inside a cardboard electro-insulating cylinder. From practical experience, in the exploitation of power transformers of 110 kV/MT in oil electro-insulating were recorded some passing disconnecting commanded by the gas protection at internal defects. In normal operation and in the optimal load, nominal currents do not require thermal secure contacts inside electrical transformers, contacts are made at the fabrication according to the projects or to repair by solder. In the case of external short circuits close to the substation, the contacts inside electrical transformers, even if they are well made in sizes of Rcontact = 10‑6 Ω, are subjected to short-circuit currents of the order of 10 kA-20 kA which lead to the dissipation of some significant second-order electric powers, 100 W-400 W, on contact. At some internal or external factors which action on electrical contacts, including electrodynamic efforts at short-circuits, these factors could be degraded over time to values in the range of 10-4 Ω to 10-5 Ω and if the action time of protection is great, on the order of seconds, power dissipation on electrical contacts achieve high values of 1,0 kW to 40,0 kW. This power leads to strong local heating, hundreds of degrees Celsius and can initiate self-ignition and burning oil in the vicinity of electro-insulating contacts with action the gas relay. Degradation of electrical contacts inside power transformers may not be limited for the duration of their operation. In order to avoid oil burn with gas release near electrical contacts, at short-circuit currents 10 kA-20 kA, we have outlined the following solutions: covering electrical contacts in fireproof materials that would avoid direct burn oil at short circuit and transmission of heat from electrical contact along the conductors with heat dissipation gradually over time, in a large volume of cooling. Flame retardant materials are: polyurethane foam, mastic, cement (concrete). In the normal condition of operation of transformer, insulating of conductors coils is with paper and insulating oil. Ignition points of its two components respectively are approximated: 135 °C heat for oil and 200 0C for paper. In the case of a faulty electrical contact, about 10-3 Ω, at short-circuit; the temperature can reach for a short time, a value of 300 °C-400 °C, which ignite the paper and also the oil. By burning oil, there are local gases that disconnect the power transformer. Securing thermal electrical contacts inside the transformer, in cardboard tube with polyurethane foams, mastik or cement, ensures avoiding gas release and also gas protection working.
Abstract: This article discusses the benefit cost analysis aspects of millimetre wavebands (mmWaves) and Super High Frequency (SHF). The devaluation along the distance of the carrier-to-noise-plus-interference ratio with the coverage distance is assessed by considering two different path loss models, the two-slope urban micro Line-of-Sight (UMiLoS) for the SHF band and the modified Friis propagation model, for frequencies above 24 GHz. The equivalent supported throughput is estimated at the 5.62, 28, 38, 60 and 73 GHz frequency bands and the influence of carrier-to-noise-plus-interference ratio in the radio and network optimization process is explored. Mostly owing to the lessening caused by the behaviour of the two-slope propagation model for SHF band, the supported throughput at this band is higher than at the millimetre wavebands only for the longest cell lengths. The benefit cost analysis of these pico-cellular networks was analysed for regular cellular topologies, by considering the unlicensed spectrum. For shortest distances, we can distinguish an optimal of the revenue in percentage terms for values of the cell length, R ≈ 10 m for the millimeter wavebands and for longest distances an optimal of the revenue can be observed at R ≈ 550 m for the 5.62 GHz. It is possible to observe that, for the 5.62 GHz band, the profit is slightly inferior than for millimetre wavebands, for the shortest Rs, and starts to increase for cell lengths approximately equal to the ratio between the break-point distance and the co-channel reuse factor, achieving a maximum for values of R approximately equal to 550 m.
Abstract: This research presents the first constant approximation
algorithm to the p-median network design problem with multiple
cable types. This problem was addressed with a single cable type and
there is a bifactor approximation algorithm for the problem. To the
best of our knowledge, the algorithm proposed in this paper is the first
constant approximation algorithm for the p-median network design
with multiple cable types. The addressed problem is a combination of
two well studied problems which are p-median problem and network
design problem. The introduced algorithm is a random sampling
approximation algorithm of constant factor which is conceived by
using some random sampling techniques form the literature. It is
based on a redistribution Lemma from the literature and a steiner tree
problem as a subproblem. This algorithm is simple, and it relies on the
notions of random sampling and probability. The proposed approach
gives an approximation solution with one constant ratio without
violating any of the constraints, in contrast to the one proposed in the
literature. This paper provides a (21 + 2)-approximation algorithm
for the p-median network design problem with multiple cable types
using random sampling techniques.
Abstract: In sports, individuals and teams are typically interested
in final rankings. Final results, such as times or distances, dictate
these rankings, also known as places. Places can be further associated
with ordered random variables, commonly referred to as order
statistics. In this work, we introduce a simple, yet accurate order
statistical ordinal regression function that predicts relay race places
with changeover-times. We call this function the Fenton-Wilkinson
Order Statistics model. This model is built on the following educated
assumption: individual leg-times follow log-normal distributions.
Moreover, our key idea is to utilize Fenton-Wilkinson approximations
of changeover-times alongside an estimator for the total number
of teams as in the notorious German tank problem. This original
place regression function is sigmoidal and thus correctly predicts
the existence of a small number of elite teams that significantly
outperform the rest of the teams. Our model also describes how place
increases linearly with changeover-time at the inflection point of the
log-normal distribution function. With real-world data from Jukola
2019, a massive orienteering relay race, the model is shown to be
highly accurate even when the size of the training set is only 5%
of the whole data set. Numerical results also show that our model
exhibits smaller place prediction root-mean-square-errors than linear
regression, mord regression and Gaussian process regression.